The material failure criteria for fiber-polymer composites have been expressed in terms of stresses or strains. Examples are the maximum stress, maximum strain, deviatoric strain energy, and tensor polynomial criteria [1], sanctioned by a worldwide comparison exercise [2, 3, 4]. Their general applicability, however, is based on criteria applicable to plastic materials, which exhibit no strain localization instability, no spurious mesh sensitivity, no material characteristic length, and no deterministic size effect.
In reality, fiber composites are quasibrittle materials (which also include concrete—as the archetypical case, tough ceramics, rocks, sea ice, rigid foams, bone, etc.). All quasibrittle materials fail by localization of softening damage into a discrete fracture. In contrast to plasticity, they exhibit a material characteristic length. This inevitably leads to a strong energetic (or non-statistical) size effect when geometrically similar structures of different sizes are compared [5, 6, 7, 8, e.g.]. On sufficiently small scale, all brittle materials behave as quasibrittle.
Two basic types of size effects must be distinguished. Here the focus is on the “Type 2” size effect, which occurs when a large notch or stress-free crack exists at maximum load. This size effect is weak for small specimens not much larger than the periodicity of the weave or the size of the representative volume element (RVE), for which it may seem that the stress or strain failure criteria work. But with increasing structure size, there is a gradual transition to the strong size effect of fracture mechanics caused by stored energy release associated with stress redistribution during damage. It may be noted that the “Type 1” size effect occurs in structures that fail right at the initiations of a macro-crack from a damaged RVE at a smooth surface in unnotched specimens, and represents a combination of deterministic and statistical. (or Weibull) size effects (omission of the deterministic aspect led to an erroneous conclusion [e.g.][9], namely that the Weibull modulus was a geometry-dependent variable rather than a material constant).
At mesh refinement, the use of stress or strain criteria inevitably causes a loss of objectivity, spurious mesh sensitivity and convergence problems [7, 10]. For this reason, as well as fundamentally, realistic failure analysis must be based on quasibrittle fracture mechanics, which evolved since its dawn in the mid 1970s into a mature and widely accepted theory. Fracture mechanics is well accepted for delamination fracture of layered two-dimensional (un-stitched) fiber-composite laminates. There is even an ASTM test to determine the corresponding fracture energy [11] (although this test has just been shown to require a correction for transitional size effect [16]).
The fact that quasibrittle fracture mechanics must apply to in-plane or flexural loading of fiber composite laminates was demonstrated by the numerous size effect tests performed, beginning in 1996 [8, 12, 13, 14, 15] on geometrically similar notched specimens. However, to many engineers and researchers the size effect tests have been unconvincing for two reasons: 1) some erroneously considered the size effect to be statistical, due to material randomness (although this is possible only for Type 1 failures); 2) others rejected the cohesive crack model because a gradual postpeak softening could never be observed in experiments. The specimens always failed explosively right after attaining the maximum load, and the load applied by the testing machine dropped suddenly to zero. The sudden drop seemed to indicate a LEFM behavior, but the LEFM clearly did not fit test data, and also suggested a snapback, but the area under the snapback curve would give a much smaller fracture energy than the LEFM testing.
A similar history occurred long ago for concrete and rock. Until the 1960s it was believed that concrete and rock explode at maximum load and the load applied by the testing machine drops suddenly to zero. Then, beginning in 1963, several researchers, including Hughes, Chapman, Hillsdorf, Rüsch, Evans and Marathe [18, 19, 20, 21] came up with the idea of using, for both tensile and compressive tests of concrete, a much stiffer loading frame and fast hydraulic servo-control. Suddenly, a gradual postpeak decline of the compressive or tensile load could be observed. Similar efforts to stabilize postpeak in compression testing of rock were made, beginning 1963, by Neville G. W. Cook and Charles Fairhurst at University of Minnesota [22, 23, 24]. The stability of postpeak was further enhanced by controlling the test electronically with a gage measuring the crack-mouth opening displacement (CMOD). A servo-controlled stiff machine of MTS Corporation was built in 1967.
This discovery opened a revolution in the mechanics of concrete and rock, and was one essential factor that prompted the development of quasibrittle fracture mechanics. The stabilizing effect of machine stiffness was mathematically demonstrated by static stability analysis in [10], which led to an equation for the required machine stiffness as a function of the maximum steepness of the postpeak load-deflection curve (see also [6]).
Unfortunately, the same measures did not work for fiber composites. The same stiff frames with fast servo-control did not suffice. The CMOD control of notched compact tension specimens and of edge-notched strips was tried at Northwestern, but did not work. Neither did the control of crack tip opening displacement (CTOD).
By way of the present application (and as documented on Jul. 4, 2016, in arXiv submission [17]), it is shown that the foregoing objection is invalid, that postpeak can be measured, in a stable test, and that quasibrittle fracture mechanics with transitional size effect is perfectly applicable to fiber-polymer composites.